Online Pricing via Stackelberg and Incentive Games in a Micro-Grid

This paper deals with the analysis and design of online pricing mechanisms in micro-grids. Two cases are studied in which the market layer is modeled as an open-loop and closed-loop dynamical system respectively. In the case of open-loop market dynamics, the price is generated as equilibrium price of a Stackelberg game with an incentive strategy. In such Stackelberg game, the leader is the energy supplier, the follower is the consumer, and the leader plays an incentive strategy. In the case of closed-loop market dynamics, the price is obtained as a function of the power supplied and the demand. A stability analysis is provided for both cases, which sheds light on the transient and steady-state behavior of the system in terms of the grids time constant, inertial, damping and synchronizing coefficients. Conditions on the parameters that guarantee asymptotic stability are obtained for both open-loop and closed-loop configurations. The findings provide an insight on the impact of the time constant and damping coefficient on the system response. The study also elucidates the ways in which the suppliers decisions influence the output values, thus contributing to clarify the interconnection between the market and physical layers in a micro-grid.